Quantitative Biology
ISBN: 9780262364409 | Copyright 0
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An introduction to the quantitative modeling of biological processes, presenting modeling approaches, methodology, practical algorithms, software tools, and examples of current research.The quantitative modeling of biological processes promises to expand biological research from a science of observation and discovery to one of rigorous prediction and quantitative analysis. The rapidly growing field of quantitative biology seeks to use biology's emerging technological and computational capabilities to model biological processes. This textbook offers an introduction to the theory, methods, and tools of quantitative biology. The book first introduces the foundations of biological modeling, focusing on some of the most widely used formalisms. It then presents essential methodology for model-guided analyses of biological data, covering such methods as network reconstruction, uncertainty quantification, and experimental design; practical algorithms and software packages for modeling biological systems; and specific examples of current quantitative biology research and related specialized methods. Most chapters offer problems, progressing from simple to complex, that test the reader's mastery of such key techniques as deterministic and stochastic simulations and data analysis. Many chapters include snippets of code that can be used to recreate analyses and generate figures related to the text. Examples are presented in the three popular computing languages: Matlab, R, and Python. A variety of online resources supplement the the text.The editors are long-time organizers of the Annual q-bio Summer School, which was founded in 2007. Through the school, the editors have helped to train more than 400 visiting students in Los Alamos, NM, Santa Fe, NM, San Diego, CA, Albuquerque, NM, and Fort Collins, CO. This book is inspired by the school's curricula, and most of the contributors have participated in the school as students, lecturers, or both.ContributorsJohn H. Abel, Roberto Bertolusso, Daniela Besozzi, Michael L. Blinov, Clive G. Bowsher, Fiona A. Chandra, Paolo Cazzaniga, Bryan C. Daniels, Bernie J. Daigle, Jr., Maciej Dobrzynski, Jonathan P. Doye, Brian Drawert, Sean Fancer, Gareth W. Fearnley, Dirk Fey, Zachary Fox, Ramon Grima, Andreas Hellander, Stefan Hellander, David Hofmann, Damian Hernandez, William S. Hlavacek, Jianjun Huang, Tomasz Jetka, Dongya Jia, Mohit Kumar Jolly, Boris N. Kholodenko, Markek Kimmel, Michal Komorowski, Ganhui Lan, Heeseob Lee, Herbert Levine, Leslie M Loew, Jason G. Lomnitz, Ard A. Louis, Grant Lythe, Carmen Molina-París, Ion I. Moraru, Andrew Mugler, Brian Munsky, Joe Natale, Ilya Nemenman, Karol Nienaltowski, Marco S. Nobile, Maria Nowicka, Sarah Olson, Alan S. Perelson, Linda R. Petzold, Sreenivasan Ponnambalam, Arya Pourzanjani, Ruy M. Ribeiro, William Raymond, William Raymond, Herbert M. Sauro, Michael A. Savageau, Abhyudai Singh, James C. Schaff, Boris M. Slepchenko, Thomas R. Sokolowski, Petr Šulc, Andrea Tangherloni, Pieter Rein ten Wolde, Philipp Thomas, Karen Tkach Tuzman, Lev S. Tsimring, Dan Vasilescu, Margaritis Voliotis, Lisa Weber
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| Contents (pg. vii) | |
| 1. Introduction to Quantitative Biology (pg. 1) | |
| 1.1 History and Overview of the q-bio Summer School (pg. 1) | |
| 1.2 Origin and Organization of this Textbook (pg. 2) | |
| 1.3 How to Use this Book (pg. 4) | |
| 1.4 Acknowledgments (pg. 6) | |
| 2. Fostering Collaborations between Experimentalists and Modelers (pg. 9) | |
| 2.1 Education (pg. 10) | |
| 2.2 Presentation (pg. 10) | |
| 2.3 Practice (pg. 11) | |
| 2.4 Attitude (pg. 11) | |
| I. Defining and Simulating Models (pg. 13) | |
| Introduction to the Simulation of Models (pg. 15) | |
| 3. Modeling with Ordinary Differential Equations (pg. 19) | |
| 3.1 Introduction (pg. 19) | |
| 3.2 A Primer to Ordinary Differential Equations (pg. 20) | |
| 3.3 From Biochemical Reactions Networks to ODEs (pg. 21) | |
| 3.4 Solving ODEs (pg. 27) | |
| 3.5 Complex Dynamic Behavior: Different Types of Solutions (pg. 33) | |
| 3.6 Detailed Balance: Thermodynamic Constraints (pg. 36) | |
| 3.7 Model Simplifications and Level of Abstraction (pg. 38) | |
| 3.8 Some Advanced Modeling Concepts (pg. 42) | |
| 3.9 Overview of Relevant Software Tools (pg. 45) | |
| 3.10 Exercises (pg. 46) | |
| 4. Modeling with Partial Differential Equations (pg. 49) | |
| 4.1 Introduction to Partial Differential Equations (pg. 49) | |
| 4.2 PDE Theory (pg. 56) | |
| 4.3 Analytical Solutions (pg. 57) | |
| 4.4 Numerical Solutions (pg. 63) | |
| 4.5 Summary and Discussion (pg. 66) | |
| 4.6 Exercises (pg. 66) | |
| 5. Stochasticity or Noise in Biochemical Reactions (pg. 71) | |
| 5.1 Introduction (pg. 71) | |
| 5.2 The Chemical Master Equation (pg. 73) | |
| 5.3 Analyzing Population Statistics with FSP Approaches (pg. 77) | |
| 5.4 Comparing CME Models to Single-Cell Data (pg. 83) | |
| 5.5 Examples (pg. 85) | |
| 5.6 Summary (pg. 91) | |
| 5.7 Exercises (pg. 92) | |
| 6. The Linear-Noise Approximation and Moment Closure Approximations for Stochastic Chemical Kinetics (pg. 95) | |
| 6.1 Introduction (pg. 95) | |
| 6.2 Stochastic Models of Biochemical Systems (pg. 96) | |
| 6.3 Time Evolution of Statistical Moments (pg. 98) | |
| 6.4 Moment Closure Methods (pg. 101) | |
| 6.5 The Linear-Noise Approximation (pg. 105) | |
| 6.6 Conclusion (pg. 111) | |
| 6.7 Exercises (pg. 112) | |
| 7. Kinetic Monte Carlo Analyses of Discrete Biomolecular Events (pg. 113) | |
| 7.1 Introduction to Stochastic Simulations (pg. 113) | |
| 7.2 Example (pg. 127) | |
| 7.3 Model Specification Using Petri Nets (pg. 128) | |
| 7.4 bioPN (pg. 131) | |
| 7.5 Exercises (pg. 135) | |
| 8. The Extra Reaction Algorithm for Stochastic Simulation of Biochemical Reaction Systems in Fluctuating Environments (pg. 137) | |
| 8.1 Introduction (pg. 137) | |
| 8.2 The Extrande Method (pg. 138) | |
| 8.3 Gene Expression with Time-Varying Transcription (pg. 142) | |
| 8.4 Discussion (pg. 145) | |
| 9. Spatial-Stochastic Simulation of Reaction-Diffusion Systems (pg. 149) | |
| 9.1 Why Spatiality Matters (pg. 150) | |
| 9.2 Brownian Dynamics Simulations with Reactions (pg. 152) | |
| 9.3 Event-Driven Schemes (pg. 161) | |
| 9.4 Recent Developments: Hybrid Schemes and Parallelization (pg. 172) | |
| 9.5 Further Reading (pg. 173) | |
| 9.6 Online Resources (pg. 173) | |
| 9.7 Summary (pg. 174) | |
| 9.8 Exercises (pg. 174) | |
| 10. Introduction to Molecular Simulation (pg. 179) | |
| 10.1 Introduction (pg. 179) | |
| 10.2 Molecular Dynamics (pg. 180) | |
| 10.3 Monte Carlo Sampling (pg. 185) | |
| 10.4 Practical Aspects of Numerical Simulations (pg. 187) | |
| 10.5 Acceleration of Equilibration and Simulating Rare Events (pg. 195) | |
| 10.6 Simulation Tools (pg. 199) | |
| 10.7 Summary (pg. 202) | |
| 10.8 Exercises (pg. 203) | |
| II. Model Development and Analysis Tools (pg. 207) | |
| Introduction to Model Development and Analysis (pg. 209) | |
| 11. Reverse-Engineering Biological Networks from Large Data Sets (pg. 213) | |
| 11.1 Lay of the Land (pg. 213) | |
| 11.2 Roles for Reverse-Engineering in Systems Biology Research (pg. 220) | |
| 11.3 Two Different Meanings of Phenomenological "Reconstruction'' (pg. 228) | |
| 11.4 Discussion (pg. 241) | |
| 11.5 Try on Your Own: Become a Reverse Engineer (pg. 244) | |
| 11.6 Exercises (pg. 245) | |
| 12. Mathematically Controlled Comparisons for Elucidation of Biological Design Principles (pg. 247) | |
| 12.1 Introduction (pg. 248) | |
| 12.2 End-Product Inhibition: Steady-State Behavior (pg. 251) | |
| 12.3 Transcriptional Autorepression: Dynamic Behavior (pg. 259) | |
| 12.4 Discussion (pg. 265) | |
| 12.5 Summary (pg. 268) | |
| 12.6 Exercises (pg. 269) | |
| 13. Parameter Estimation, Sloppiness, and Model Identifiability (pg. 271) | |
| 13.1 Introduction (pg. 272) | |
| 13.2 Formulating the Parameter Estimation Problem (pg. 273) | |
| 13.3 Solving the Inverse Problem: Nonlinear Optimization (pg. 277) | |
| 13.4 Model Identifiability: Parameters Cannot Always Be Estimated (pg. 279) | |
| 13.5 Precision of Parameter Estimates Using Sensitivity Analysis (pg. 283) | |
| 13.6 Parameter Estimation in the Wild: Practicalities (pg. 289) | |
| 13.7 Summary (pg. 290) | |
| 13.8 Exercises (pg. 290) | |
| 14. Sensitivity Analysis (pg. 293) | |
| 14.1 Introduction (pg. 293) | |
| 14.2 Theoretical Concepts (pg. 294) | |
| 14.3 Applications of the Sensitivity Analysis (pg. 305) | |
| 14.4 Summary (pg. 315) | |
| 14.5 Exercises (pg. 316) | |
| 15. Experimental Design (pg. 321) | |
| 15.1 Introduction (pg. 321) | |
| 15.2 General Framework (pg. 322) | |
| 15.3 Frequentist Approach (pg. 323) | |
| 15.4 Bayesian Approach (pg. 326) | |
| 15.5 Asymptotic Equivalency (pg. 327) | |
| 15.6 Applications of Experiment Design (pg. 328) | |
| 15.7 Discussion (pg. 334) | |
| 15.8 Exercises (pg. 335) | |
| 16. Bayesian Parameter Estimation and Markov Chain Monte Carlo (pg. 339) | |
| 16.1 Introduction (pg. 339) | |
| 16.2 Likelihood-Based Inference (pg. 340) | |
| 16.3 Bayesian Inference (pg. 343) | |
| 16.4 Markov Chain Monte Carlo for Bayesian Inference (pg. 345) | |
| 16.5 Likelihood-Free Methods for Bayesian Inference (pg. 350) | |
| 16.6 Exercises (pg. 355) | |
| 17. Uses of Bifurcation Analysis in Understanding Cellular Decision-Making Dongya Jia, Mohit Kumar Jolly, and Herbert Levine (pg. 357) | |
| 17.1 Introduction (pg. 357) | |
| 17.2 Basic Concepts in Bifurcation Analysis (pg. 360) | |
| 17.3 Bifurcations in One Dimension (pg. 363) | |
| 17.4 Using Bifurcation Theory to Understand Cellular Decision-Making (pg. 365) | |
| 17.5 Bifurcation Theory in Parameter Sensitivity Analyses (pg. 375) | |
| 17.6 Bifurcation Theory and Experimental Testing with Flow Cytometry (pg. 377) | |
| 17.7 Conclusions (pg. 377) | |
| 17.8 Exercises (pg. 378) | |
| 18. Performance Measures for Stochastic Processes and the Matrix-Analytic Approach (pg. 379) | |
| 18.1 Introduction (pg. 379) | |
| 18.2 Analysis of the Stochastic Descriptors: An Application to VEGFR2/VEGF-A Interaction and Signaling (pg. 382) | |
| 18.3 Numerical Results (pg. 392) | |
| 18.4 Discussion (pg. 394) | |
| III. Modeling in Practice (pg. 401) | |
| Introduction to Computational Modeling Tools in Quantitative Biology (pg. 403) | |
| 19. Setting Up and Simulating ODE Models (pg. 405) | |
| 19.1 Introduction to Tellurium: A Python-Based Platform (pg. 405) | |
| 19.2 Building and Simulating a Model (pg. 406) | |
| 19.3 Antimony: Network Description Language (pg. 409) | |
| 19.4 Running Simulations (pg. 411) | |
| 19.5 Fitting Models to Data (pg. 413) | |
| 19.6 Validation, Validation, and More Validation (pg. 416) | |
| 19.7 Publishing a Reproducible Model (pg. 418) | |
| 19.8 Illustrative Examples (pg. 420) | |
| 19.9 Summary (pg. 421) | |
| 19.10 Availability of Software (pg. 421) | |
| 19.11 Exercises (pg. 421) | |
| 20. Accelerating Stochastic Simulations Using Graphics Processing Units (pg. 423) | |
| 20.1 Introduction (pg. 423) | |
| 20.2 Methods (pg. 426) | |
| 20.3 Example (pg. 437) | |
| 20.4 Discussion (pg. 440) | |
| 21. Rule-Based Modeling Using Virtual Cell (VCELL) (pg. 441) | |
| 21.1 Introduction (pg. 441) | |
| 21.2 Rule-Based Modeling in VCell (pg. 444) | |
| 21.3 Physiology (pg. 445) | |
| 21.4 Rule-Based Modeling in VCell: Applications and Simulations (pg. 451) | |
| 21.5 Conclusions (pg. 453) | |
| 21.6 Additional Information (pg. 454) | |
| 22. Spatial Modeling of Cellular Systems with VCELL (pg. 455) | |
| 22.1 Introduction (pg. 455) | |
| 22.2 Compartmental Models: Sizes of Cellular Compartments May Matter even if Diffusion is Fast on the Time Scale of Reactions (pg. 456) | |
| 22.3 Reaction-Diffusion in Explicit Geometries: Why Space Should Be Explicitly Modeled (pg. 459) | |
| 22.4 Numerical Approaches to Spatial Models Arising in Cell Biology (pg. 462) | |
| 22.5 Conclusion (pg. 468) | |
| 23. Stochastic Simulation of Well-Mixed and Spatially Inhomogeneous Biochemical Systems (pg. 469) | |
| 23.1 Introduction (pg. 469) | |
| 23.2 Algorithms (pg. 471) | |
| 23.3 Software for Stochastic Simulation of Biochemical Systems (pg. 474) | |
| 23.4 Examples (pg. 477) | |
| 23.5 Discussion (pg. 480) | |
| 23.6 Summary (pg. 483) | |
| 23.7 Exercises (pg. 483) | |
| 24. Spatial Stochastic Modeling with MCell and CellBlender (pg. 485) | |
| 24.1 Introduction: Why Stochastic Spatial Modeling? (pg. 485) | |
| 24.2 A Brief Overview of MCell (pg. 488) | |
| 24.3 Getting Started with CellBlender and MCell (pg. 493) | |
| 24.4 Simulating Free Molecular Diffusion (pg. 495) | |
| 24.5 Restricting Diffusion by Defining Meshes (pg. 497) | |
| 24.6 Simulating Bimolecular Reactions in a Volume (pg. 499) | |
| 24.7 Simulating Molecules and Reactions on Surfaces (pg. 504) | |
| 24.8 Extended Exercise: A Density-Dependent Switch (pg. 509) | |
| 24.9 Concluding Remarks (pg. 511) | |
| IV. Example Models and Specialized Methods (pg. 513) | |
| Introduction to Examples in Quantitative Biology (pg. 515) | |
| 25. The Use of Linear Analysis and Sensitivity Functions in Exploring Trade-Offs in Biology: Applications to Glycolytic Oscillations (pg. 519) | |
| 25.1 Introduction (pg. 519) | |
| 25.2 Analysis of the Minimal Model of Glycolysis (pg. 524) | |
| 25.3 Discussion (pg. 528) | |
| 26. Models of Bacterial Chemotaxis (pg. 531) | |
| 26.1 Introduction: The E. coli Chemotaxis Network (pg. 531) | |
| 26.2 Ising-Type Description of the E. coli Chemotactic Process (pg. 536) | |
| 26.3 Summary (pg. 544) | |
| 27. Modeling Viral Dynamics (pg. 545) | |
| 27.1 Introduction: Basic Biology of HIV Infection (pg. 546) | |
| 27.2 A Simple Model of HIV Dynamics (pg. 547) | |
| 27.3 Basic Principles of Viral Dynamics and Drug Treatment (pg. 549) | |
| 27.4 Using Modeling to Gain Further Insight into HIV-1 Biology (pg. 551) | |
| 27.5 Other Model Applications and Extensions (pg. 557) | |
| 27.6 Further Reading (pg. 561) | |
| 27.7 Exercises (pg. 561) | |
| 28. Stochastic Modeling of Gene Expression, Protein Modification, and Polymerization (pg. 563) | |
| 28.1 Introduction (pg. 563) | |
| 28.2 Gene Expression (pg. 564) | |
| 28.3 Protein Modification (pg. 572) | |
| 28.4 Polymerization (pg. 574) | |
| 28.5 Interactions (pg. 577) | |
| 28.6 More Complex Phenomena (pg. 579) | |
| 28.7 Summary and Outlook (pg. 580) | |
| 28.8 Exercises (pg. 580) | |
| 29. Modeling Cell-Fate Decisions in Biological Systems: Bacteriophage, Hematopoietic Stem Cells, Epithelial-to-Mesenchymal Transition, and Beyond (pg. 583) | |
| 29.1 Introduction (pg. 583) | |
| 29.2 Lysis/Lysogeny Decision in Lambda Phage (pg. 585) | |
| 29.3 Cell-Fate Decisions in Hematopoietic Stem Cell System (pg. 588) | |
| 29.4 Epithelial-to-Mesenchymal Transition (pg. 590) | |
| 29.5 Notch-Delta-Jagged Signaling (pg. 594) | |
| 29.6 Which Modeling Framework to Use and When? (pg. 597) | |
| 29.7 Exercises (pg. 598) | |
| 30. Tutorial on the Identification of Gene Regulation Models from Single-Cell Data (pg. 599) | |
| 30.1 Outline of Our Approach (pg. 599) | |
| 30.2 Gene Regulation Model Description (pg. 600) | |
| 30.3 Exercise Tasks (pg. 603) | |
| 30.4 Exercise Results and GUI (pg. 614) | |
| 30.5 Summary and Conclusions (pg. 616) | |
| References (pg. 617) | |
| Contributors (pg. 695) | |
| Index (pg. 701) | |
| Contents (pg. vii) | |
| 1. Introduction to Quantitative Biology (pg. 1) | |
| 1.1 History and Overview of the q-bio Summer School (pg. 1) | |
| 1.2 Origin and Organization of this Textbook (pg. 2) | |
| 1.3 How to Use this Book (pg. 4) | |
| 1.4 Acknowledgments (pg. 6) | |
| 2. Fostering Collaborations between Experimentalists and Modelers (pg. 9) | |
| 2.1 Education (pg. 10) | |
| 2.2 Presentation (pg. 10) | |
| 2.3 Practice (pg. 11) | |
| 2.4 Attitude (pg. 11) | |
| I. Defining and Simulating Models (pg. 13) | |
| Introduction to the Simulation of Models (pg. 15) | |
| 3. Modeling with Ordinary Differential Equations (pg. 19) | |
| 3.1 Introduction (pg. 19) | |
| 3.2 A Primer to Ordinary Differential Equations (pg. 20) | |
| 3.3 From Biochemical Reactions Networks to ODEs (pg. 21) | |
| 3.4 Solving ODEs (pg. 27) | |
| 3.5 Complex Dynamic Behavior: Different Types of Solutions (pg. 33) | |
| 3.6 Detailed Balance: Thermodynamic Constraints (pg. 36) | |
| 3.7 Model Simplifications and Level of Abstraction (pg. 38) | |
| 3.8 Some Advanced Modeling Concepts (pg. 42) | |
| 3.9 Overview of Relevant Software Tools (pg. 45) | |
| 3.10 Exercises (pg. 46) | |
| 4. Modeling with Partial Differential Equations (pg. 49) | |
| 4.1 Introduction to Partial Differential Equations (pg. 49) | |
| 4.2 PDE Theory (pg. 56) | |
| 4.3 Analytical Solutions (pg. 57) | |
| 4.4 Numerical Solutions (pg. 63) | |
| 4.5 Summary and Discussion (pg. 66) | |
| 4.6 Exercises (pg. 66) | |
| 5. Stochasticity or Noise in Biochemical Reactions (pg. 71) | |
| 5.1 Introduction (pg. 71) | |
| 5.2 The Chemical Master Equation (pg. 73) | |
| 5.3 Analyzing Population Statistics with FSP Approaches (pg. 77) | |
| 5.4 Comparing CME Models to Single-Cell Data (pg. 83) | |
| 5.5 Examples (pg. 85) | |
| 5.6 Summary (pg. 91) | |
| 5.7 Exercises (pg. 92) | |
| 6. The Linear-Noise Approximation and Moment Closure Approximations for Stochastic Chemical Kinetics (pg. 95) | |
| 6.1 Introduction (pg. 95) | |
| 6.2 Stochastic Models of Biochemical Systems (pg. 96) | |
| 6.3 Time Evolution of Statistical Moments (pg. 98) | |
| 6.4 Moment Closure Methods (pg. 101) | |
| 6.5 The Linear-Noise Approximation (pg. 105) | |
| 6.6 Conclusion (pg. 111) | |
| 6.7 Exercises (pg. 112) | |
| 7. Kinetic Monte Carlo Analyses of Discrete Biomolecular Events (pg. 113) | |
| 7.1 Introduction to Stochastic Simulations (pg. 113) | |
| 7.2 Example (pg. 127) | |
| 7.3 Model Specification Using Petri Nets (pg. 128) | |
| 7.4 bioPN (pg. 131) | |
| 7.5 Exercises (pg. 135) | |
| 8. The Extra Reaction Algorithm for Stochastic Simulation of Biochemical Reaction Systems in Fluctuating Environments (pg. 137) | |
| 8.1 Introduction (pg. 137) | |
| 8.2 The Extrande Method (pg. 138) | |
| 8.3 Gene Expression with Time-Varying Transcription (pg. 142) | |
| 8.4 Discussion (pg. 145) | |
| 9. Spatial-Stochastic Simulation of Reaction-Diffusion Systems (pg. 149) | |
| 9.1 Why Spatiality Matters (pg. 150) | |
| 9.2 Brownian Dynamics Simulations with Reactions (pg. 152) | |
| 9.3 Event-Driven Schemes (pg. 161) | |
| 9.4 Recent Developments: Hybrid Schemes and Parallelization (pg. 172) | |
| 9.5 Further Reading (pg. 173) | |
| 9.6 Online Resources (pg. 173) | |
| 9.7 Summary (pg. 174) | |
| 9.8 Exercises (pg. 174) | |
| 10. Introduction to Molecular Simulation (pg. 179) | |
| 10.1 Introduction (pg. 179) | |
| 10.2 Molecular Dynamics (pg. 180) | |
| 10.3 Monte Carlo Sampling (pg. 185) | |
| 10.4 Practical Aspects of Numerical Simulations (pg. 187) | |
| 10.5 Acceleration of Equilibration and Simulating Rare Events (pg. 195) | |
| 10.6 Simulation Tools (pg. 199) | |
| 10.7 Summary (pg. 202) | |
| 10.8 Exercises (pg. 203) | |
| II. Model Development and Analysis Tools (pg. 207) | |
| Introduction to Model Development and Analysis (pg. 209) | |
| 11. Reverse-Engineering Biological Networks from Large Data Sets (pg. 213) | |
| 11.1 Lay of the Land (pg. 213) | |
| 11.2 Roles for Reverse-Engineering in Systems Biology Research (pg. 220) | |
| 11.3 Two Different Meanings of Phenomenological "Reconstruction'' (pg. 228) | |
| 11.4 Discussion (pg. 241) | |
| 11.5 Try on Your Own: Become a Reverse Engineer (pg. 244) | |
| 11.6 Exercises (pg. 245) | |
| 12. Mathematically Controlled Comparisons for Elucidation of Biological Design Principles (pg. 247) | |
| 12.1 Introduction (pg. 248) | |
| 12.2 End-Product Inhibition: Steady-State Behavior (pg. 251) | |
| 12.3 Transcriptional Autorepression: Dynamic Behavior (pg. 259) | |
| 12.4 Discussion (pg. 265) | |
| 12.5 Summary (pg. 268) | |
| 12.6 Exercises (pg. 269) | |
| 13. Parameter Estimation, Sloppiness, and Model Identifiability (pg. 271) | |
| 13.1 Introduction (pg. 272) | |
| 13.2 Formulating the Parameter Estimation Problem (pg. 273) | |
| 13.3 Solving the Inverse Problem: Nonlinear Optimization (pg. 277) | |
| 13.4 Model Identifiability: Parameters Cannot Always Be Estimated (pg. 279) | |
| 13.5 Precision of Parameter Estimates Using Sensitivity Analysis (pg. 283) | |
| 13.6 Parameter Estimation in the Wild: Practicalities (pg. 289) | |
| 13.7 Summary (pg. 290) | |
| 13.8 Exercises (pg. 290) | |
| 14. Sensitivity Analysis (pg. 293) | |
| 14.1 Introduction (pg. 293) | |
| 14.2 Theoretical Concepts (pg. 294) | |
| 14.3 Applications of the Sensitivity Analysis (pg. 305) | |
| 14.4 Summary (pg. 315) | |
| 14.5 Exercises (pg. 316) | |
| 15. Experimental Design (pg. 321) | |
| 15.1 Introduction (pg. 321) | |
| 15.2 General Framework (pg. 322) | |
| 15.3 Frequentist Approach (pg. 323) | |
| 15.4 Bayesian Approach (pg. 326) | |
| 15.5 Asymptotic Equivalency (pg. 327) | |
| 15.6 Applications of Experiment Design (pg. 328) | |
| 15.7 Discussion (pg. 334) | |
| 15.8 Exercises (pg. 335) | |
| 16. Bayesian Parameter Estimation and Markov Chain Monte Carlo (pg. 339) | |
| 16.1 Introduction (pg. 339) | |
| 16.2 Likelihood-Based Inference (pg. 340) | |
| 16.3 Bayesian Inference (pg. 343) | |
| 16.4 Markov Chain Monte Carlo for Bayesian Inference (pg. 345) | |
| 16.5 Likelihood-Free Methods for Bayesian Inference (pg. 350) | |
| 16.6 Exercises (pg. 355) | |
| 17. Uses of Bifurcation Analysis in Understanding Cellular Decision-Making Dongya Jia, Mohit Kumar Jolly, and Herbert Levine (pg. 357) | |
| 17.1 Introduction (pg. 357) | |
| 17.2 Basic Concepts in Bifurcation Analysis (pg. 360) | |
| 17.3 Bifurcations in One Dimension (pg. 363) | |
| 17.4 Using Bifurcation Theory to Understand Cellular Decision-Making (pg. 365) | |
| 17.5 Bifurcation Theory in Parameter Sensitivity Analyses (pg. 375) | |
| 17.6 Bifurcation Theory and Experimental Testing with Flow Cytometry (pg. 377) | |
| 17.7 Conclusions (pg. 377) | |
| 17.8 Exercises (pg. 378) | |
| 18. Performance Measures for Stochastic Processes and the Matrix-Analytic Approach (pg. 379) | |
| 18.1 Introduction (pg. 379) | |
| 18.2 Analysis of the Stochastic Descriptors: An Application to VEGFR2/VEGF-A Interaction and Signaling (pg. 382) | |
| 18.3 Numerical Results (pg. 392) | |
| 18.4 Discussion (pg. 394) | |
| III. Modeling in Practice (pg. 401) | |
| Introduction to Computational Modeling Tools in Quantitative Biology (pg. 403) | |
| 19. Setting Up and Simulating ODE Models (pg. 405) | |
| 19.1 Introduction to Tellurium: A Python-Based Platform (pg. 405) | |
| 19.2 Building and Simulating a Model (pg. 406) | |
| 19.3 Antimony: Network Description Language (pg. 409) | |
| 19.4 Running Simulations (pg. 411) | |
| 19.5 Fitting Models to Data (pg. 413) | |
| 19.6 Validation, Validation, and More Validation (pg. 416) | |
| 19.7 Publishing a Reproducible Model (pg. 418) | |
| 19.8 Illustrative Examples (pg. 420) | |
| 19.9 Summary (pg. 421) | |
| 19.10 Availability of Software (pg. 421) | |
| 19.11 Exercises (pg. 421) | |
| 20. Accelerating Stochastic Simulations Using Graphics Processing Units (pg. 423) | |
| 20.1 Introduction (pg. 423) | |
| 20.2 Methods (pg. 426) | |
| 20.3 Example (pg. 437) | |
| 20.4 Discussion (pg. 440) | |
| 21. Rule-Based Modeling Using Virtual Cell (VCELL) (pg. 441) | |
| 21.1 Introduction (pg. 441) | |
| 21.2 Rule-Based Modeling in VCell (pg. 444) | |
| 21.3 Physiology (pg. 445) | |
| 21.4 Rule-Based Modeling in VCell: Applications and Simulations (pg. 451) | |
| 21.5 Conclusions (pg. 453) | |
| 21.6 Additional Information (pg. 454) | |
| 22. Spatial Modeling of Cellular Systems with VCELL (pg. 455) | |
| 22.1 Introduction (pg. 455) | |
| 22.2 Compartmental Models: Sizes of Cellular Compartments May Matter even if Diffusion is Fast on the Time Scale of Reactions (pg. 456) | |
| 22.3 Reaction-Diffusion in Explicit Geometries: Why Space Should Be Explicitly Modeled (pg. 459) | |
| 22.4 Numerical Approaches to Spatial Models Arising in Cell Biology (pg. 462) | |
| 22.5 Conclusion (pg. 468) | |
| 23. Stochastic Simulation of Well-Mixed and Spatially Inhomogeneous Biochemical Systems (pg. 469) | |
| 23.1 Introduction (pg. 469) | |
| 23.2 Algorithms (pg. 471) | |
| 23.3 Software for Stochastic Simulation of Biochemical Systems (pg. 474) | |
| 23.4 Examples (pg. 477) | |
| 23.5 Discussion (pg. 480) | |
| 23.6 Summary (pg. 483) | |
| 23.7 Exercises (pg. 483) | |
| 24. Spatial Stochastic Modeling with MCell and CellBlender (pg. 485) | |
| 24.1 Introduction: Why Stochastic Spatial Modeling? (pg. 485) | |
| 24.2 A Brief Overview of MCell (pg. 488) | |
| 24.3 Getting Started with CellBlender and MCell (pg. 493) | |
| 24.4 Simulating Free Molecular Diffusion (pg. 495) | |
| 24.5 Restricting Diffusion by Defining Meshes (pg. 497) | |
| 24.6 Simulating Bimolecular Reactions in a Volume (pg. 499) | |
| 24.7 Simulating Molecules and Reactions on Surfaces (pg. 504) | |
| 24.8 Extended Exercise: A Density-Dependent Switch (pg. 509) | |
| 24.9 Concluding Remarks (pg. 511) | |
| IV. Example Models and Specialized Methods (pg. 513) | |
| Introduction to Examples in Quantitative Biology (pg. 515) | |
| 25. The Use of Linear Analysis and Sensitivity Functions in Exploring Trade-Offs in Biology: Applications to Glycolytic Oscillations (pg. 519) | |
| 25.1 Introduction (pg. 519) | |
| 25.2 Analysis of the Minimal Model of Glycolysis (pg. 524) | |
| 25.3 Discussion (pg. 528) | |
| 26. Models of Bacterial Chemotaxis (pg. 531) | |
| 26.1 Introduction: The E. coli Chemotaxis Network (pg. 531) | |
| 26.2 Ising-Type Description of the E. coli Chemotactic Process (pg. 536) | |
| 26.3 Summary (pg. 544) | |
| 27. Modeling Viral Dynamics (pg. 545) | |
| 27.1 Introduction: Basic Biology of HIV Infection (pg. 546) | |
| 27.2 A Simple Model of HIV Dynamics (pg. 547) | |
| 27.3 Basic Principles of Viral Dynamics and Drug Treatment (pg. 549) | |
| 27.4 Using Modeling to Gain Further Insight into HIV-1 Biology (pg. 551) | |
| 27.5 Other Model Applications and Extensions (pg. 557) | |
| 27.6 Further Reading (pg. 561) | |
| 27.7 Exercises (pg. 561) | |
| 28. Stochastic Modeling of Gene Expression, Protein Modification, and Polymerization (pg. 563) | |
| 28.1 Introduction (pg. 563) | |
| 28.2 Gene Expression (pg. 564) | |
| 28.3 Protein Modification (pg. 572) | |
| 28.4 Polymerization (pg. 574) | |
| 28.5 Interactions (pg. 577) | |
| 28.6 More Complex Phenomena (pg. 579) | |
| 28.7 Summary and Outlook (pg. 580) | |
| 28.8 Exercises (pg. 580) | |
| 29. Modeling Cell-Fate Decisions in Biological Systems: Bacteriophage, Hematopoietic Stem Cells, Epithelial-to-Mesenchymal Transition, and Beyond (pg. 583) | |
| 29.1 Introduction (pg. 583) | |
| 29.2 Lysis/Lysogeny Decision in Lambda Phage (pg. 585) | |
| 29.3 Cell-Fate Decisions in Hematopoietic Stem Cell System (pg. 588) | |
| 29.4 Epithelial-to-Mesenchymal Transition (pg. 590) | |
| 29.5 Notch-Delta-Jagged Signaling (pg. 594) | |
| 29.6 Which Modeling Framework to Use and When? (pg. 597) | |
| 29.7 Exercises (pg. 598) | |
| 30. Tutorial on the Identification of Gene Regulation Models from Single-Cell Data (pg. 599) | |
| 30.1 Outline of Our Approach (pg. 599) | |
| 30.2 Gene Regulation Model Description (pg. 600) | |
| 30.3 Exercise Tasks (pg. 603) | |
| 30.4 Exercise Results and GUI (pg. 614) | |
| 30.5 Summary and Conclusions (pg. 616) | |
| References (pg. 617) | |
| Contributors (pg. 695) | |
| Index (pg. 701) | |
|
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